Ole Gunnar Solskjaer is desperate to shake up his misfiring strike force this summer and the 22-year-old French striker is one name being considered.
Dembele only moved from Celtic to Lyon last summer but has enjoyed a prolific season, scoring 22 times for the French club in all competitions.
According to The Sun, United are willing to offer as much as £40million for the former Fulham striker.
He is under contract for another four years but Solskjaer has reportedly started the process of background checks ahead of a potential approach.
Earlier this month, according to French newspaper L’Equipe, United made clear their interest in Dembele to Lyon.